We introduce Localized Components Analysis (LoCA) for describing surface shape variation in an ensemble of biomedical objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicitly for localized components and allows a flexible trade-off between localized and concise representations. Experiments comparing LoCA to a variety of competing shape representation methods on 2D and 3D shape ensembles establish the superior ability of LoCA to modulate the locality-conciseness tradeoff and generate shape components corresponding to intuitive modes of shape variation. Our formulation of locality in terms of compatibility between pairs of surface points is shown to be flexible enough to enable spatially-localized shape descriptions with attractive higher-order properties such as spatial symmetry.